Recall that a phone lattice is a type of state diagram, i.e. a directed graph where each node represents a state of a system. A phone lattice has exactly one letter on each edge. Each path from the start node to a final/end node represents a word. Draw a phone lattice representing exactly the following set of words, using a single start node and no more than 9 nodes total.
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- When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…
- Write a java program that takes a matrix representing an undirected graph (connectivity matrix) and finds the minimum spanning tree (using kruskal's or prim's algo.) of that graph and then print it graphically ( Graphical user interface should be used)The Graph Data Structure is made up of nodes and edges. (A Tree Data Structure is a special kind of a Graph Data Structure). A Graph may be represented by an Adjacency Matrix or an Adjacency List. Through this exercise, you should be able to have a better grasp the Adjacency Matrix concept. You are expected to read about the Adjacency Matrix concept as well as the Adjacency List concept. Suppose the vertices A, B, C, D, E, F, G and H of a Graph are mapped to row and column indices(0,1,2,3,4,5,6,and 7) of a matrix (i.e. 2-dimensional array) as shown in the following table. Vertex of Graph Index in the 2-D Array Adjacency Matrix Representation of Graph A B 2 F 6. H 7 Suppose further, that the following is an Adjacency Matrix representing the Graph. 3 4 5. 6. 7 0. 1 1 1 1 01 1 01 1. 3 14 1 1 1 6. 1 Exercise: Show/Draw the Graph that is represented by the above Adjacency matrix. Upload the document that contains your result. (Filename: AdjacencyMatrixExercise.pdf) Notes: -The nodes of the…When we learn about Graph Traversals, one question that I'm sometimes asked by students is why we need them at all. Consider the two implementation strategies for graphs that we learned about previously: an adjacency matrix and adjacency lists. Both of them include a separate array-based structure in which information about every vertex is stored. So if our only goal is to visit every vertex, we can do that by just iterating through that array-based structure. If visiting every vertex is as easy as iterating through them, then why do we need graph traversal algorithms such as depth-first and breadth-first? What purpose do they serve that just iterating through the vertices one at a time, without regard for the presence of edges, wouldn't? JAVA PROGRAMMING
- Consider a maze represented by a matrix of m rows and n columns with obstacles (see the figure below). A cell with a value = -1 is an obstacle that cannot be overcome. The goal is to start from cell [0, 0] and reach the last cell [m-1, n-1]. This may be possible by taking several paths. Count the number of these paths. The movement is allowed from cells (i+ 1, j) and (i, j+ 1) only. -1 -1 Provide two solutions, one iterative and one recursive to the above problem.1.Attached is a sample data frame of tweets data extracted between 2016-2022. I want a python code to show the distribution of tweets per year over that time period. 2. I want a python code of a force directed graph of a user like CABI_Plantwise, where i can see the interactions with that accountFor the graph in the attached picture, find the set V of vertices. Do not forget to enclose the elements in a pair of braces and put a space after each comma separating elements. Your answer should look like this: V= (a, b, c). It is understandable that the subscript is written just beside the letter like a1, a2, a3. Please write the elements in increasing order of subscript. U3 e3 e4 v4 Write your answer: For the graph in the attached picture, find the set E of edges. Do not forget to enclose the olements in a pair of braces and put a space after each comma separating elements. Your answer should look like this: Eafa, b, c). It is understandable that the subscript is written just beside the letter like a1, a2, a3. Please write the elements in increasing order of subscript. es e6 e2 V4 Write your answer.
- How do we solve this problem in Java language? Thank you! We can describe the physical structure of some designs using an undirected graph. We’ll say vertex i is part of a triangle if i has two different neighbors j and k such that j and k are neighbors of each other. For this problem, find weak vertices in graphs – those vertices that is not part of any triangle. Figure 1: An illustration of the weak vertices (which are shaded) from the sample input graph. Input Input consists of up to 100 graphs. Each starts with an integer, 1 ≤ n ≤ 20, giving the number of vertices in the graph. Next come n lines with n integers on each line, which describe an n×n adjacency matrix for the graph. Vertices are numbered from 0 to n−1. If the adjacency matrix contains a one at row r, column c (where 0 ≤ r, c ≤ n−1), it means that there is an edge from vertex r to vertex c. Since the graph is undirected, the adjacency matrix is symmetric. The end of input is marked by a value of −1 for n. Output For…Write a program (WAP) to create an undirected graph using adjacency matrix representation.Number of nodes and edges should be taken from the user. After creating the graph, performfollowing operations: (i) Search a node. Take the node number from the user. If the node is found then print its associatededges.(ii) Insert a node in the graph.(iii) Insert an edge in the graph. Take the node numbers from the user between which the edge is tobe inserted.(iv) Delete a node from the graph. Take the node number to be deleted from the user.(v) Apply DFS on the graph and print the graph traversal.(vi) Apply BFS on the graph and print the graph traversal.Solve the above problem using adjacency list representation.Given a graph data structure: G = (V,E) where, V = {A, B, C, D, E } E = { (A,B), (A,D), (B,D), (B,C), (D,E) } a) Draw the graph G. b) Draw all spanning trees of the graph G, which are also “linear” (each graph node has no more than two neighbors).